I know what you mean. I was disappointed by both the 3CX CRM Integration and the one provided by Zammad so I ended up with two somewhat pragmatic solutions.
First, you have WAY more possibilities when using the 3CX web client API. It’s unofficial, but seems very well done and it’s rather simple. Get started here: https://www.npmjs.com/package/@3cx/api
It’s easy to add more commands, like polling the currently active calls, which is what I’m using to show caller information while ringing.
For Zammad I’m using a Electron shell that allows me to remote control / enhance the UI - like pre-filling a new ticket during a call.